Method and apparatus to reduce RF power deposition during MR data acquisition

ABSTRACT

A system composed of multiple transmit coils with corresponding RF pulse synthesizers and amplifiers is disclosed. A method of designing RF pulses specific to each transmit coil to dynamically control RF power deposition across an imaging volume is also disclosed, where parallel excitation with the transmit coils allows for management of RF power deposition on a subject while facilitating faithful production of a desired excitation profile. The present invention also supports reduction in scan time and is applicable to any coil array geometry.

BACKGROUND OF THE INVENTION

The present invention relates generally to MR imaging and, moreparticularly, to a method and apparatus of parallel excitation by atransmit coil array to realize a desired excitation profile. The presentinvention further relates to a parallel excitation pulse design methodthat accounts for mutual coupling between coils of the coil array andapplies to any coil geometry. The present invention is further directedto targeted RF excitation across an imaging volume to reduce RF powerdeposition on a subject.

When a substance such as human tissue is subjected to a uniform magneticfield (polarizing field B₀), the individual magnetic moments of thespins in the tissue attempt to align with this polarizing field, butprecess about it in random order at their characteristic Larmorfrequency. If the substance, or tissue, is subjected to a magnetic field(excitation field B₁) which is in the x-y plane and which is near theLarmor frequency, the net aligned moment, or “longitudinalmagnetization”, M_(Z), may be rotated, or “tipped”, into the x-y planeto produce a net transverse magnetic moment M_(t). A signal is emittedby the excited spins after the excitation signal B₁ is terminated andthis signal may be received and processed to form an image.

When utilizing these signals to produce images, magnetic field gradients(G_(x), G_(y), and G_(z)) are employed. Typically, the region to beimaged is scanned by a sequence of measurement cycles in which thesegradients vary according to the particular localization method beingused. The resulting set of received NMR signals are digitized andprocessed to reconstruct the image using one of many well knownreconstruction techniques.

Spatially selective excitation is widely used in MR imaging to inducetransverse magnetization while limiting the size of thesignal-contributing volume. Slice-selective excitation, the mostcommonly used, confines the signal-contributing volume to a fixed slicethat simplifies spatial encoding during signal acquisition to reducedata acquisition or scan time. Multi-dimensional excitation thatproduces localization along more than one dimension has been used tofurther this reduction in scan time. For example, localizedspectroscopy, reduced-FOV scan of a region of interest, imaging of atarget anatomy of unique shape, and echo planar imaging (EPI) with ashortened echo train length are applications usually implemented becauseof their support of reduced scan times. In addition, profile (flip,phase and frequency) control across a sizeable volume with selectiveexcitation has been exploited to improve excitation profile fidelity inthe presence of B₀ inhomogeneity or gradient non-linearity, and toreduce susceptibility artifacts.

Selective excitation is commonly implemented with a single transmit coilthat transmits across an entire volume and produces a relatively uniformB₁ field, e.g., a birdcage coil. Highly efficient pulse algorithms havebeen developed for designing excitation pulses that suit such aconfiguration. Notwithstanding the advantages achieved by these pulsedesign tools, technical difficulties remain. Issues with excitationpulse duration, excitation profile accuracy, and RF power absorption(SAR) represent some of the outstanding challenges in a variety ofapplications. Compared to 1D excitation, flexible profile control alongmultiple dimensions with 2D or 3D excitation entails intensified pulsingactivity and often requires powerful gradients to keep pulse duration incheck. This limitation hinders applications of multi-dimensionalexcitation on scanners with general-purpose gradients. Substantialsubject-dependency of B₁ field, resulting from increased wave behaviorand source-subject interaction at high frequencies, may also contributeto the difficulty of excitation profile control. An elevated rate of RFpower deposition at high frequencies represents yet another factor thathas a significant impact on the design and application of RF transmitmodules and/or excitation pulses.

It would therefore be desirable to have a system and method capable ofrealizing desired excitation profiles and reducing RF power depositionby the means of a parallel transmit element architecture.

BRIEF DESCRIPTION OF THE INVENTION

The present invention provides a system and method of independentlycontrolling transmit coils of a transmit coil array to conduct RFexcitation in an imaging volume that overcomes the aforementioneddrawbacks.

The present invention is directed to the acceleration ofmulti-dimensional excitation and control of SAR through the orchestrateddriving of multiple transmit coils. The present invention emphasizes thecoordination of multiple transmit elements to effect appropriate B₁spatiotemporal variations in a composite B₁ field in order toeffectively manage RF power absorption and multi-dimensional pulselength while facilitating faithful production of desired excitationprofiles. The present invention is also directed to the design ofparallel excitation pulses with spatial and spatial-frequency domainweighting.

Therefore, in accordance with one aspect, the invention is embodied in acomputer program stored on a computer readable storage medium and havinginstructions which, when executed by a computer, cause the computeracquire a B₁ field map for each transmit coil of a transmit coil arrayand determine from the B₁ field maps a spatiotemporal variation of acomposite B₁ field. The computer is further caused to generate an RFpulsing sequence tailored to each respective transmit coil such that RFpower deposition during MR imaging is reduced.

According to another aspect, the present invention includes an MRIapparatus comprising a magnetic resonance imaging (MRI) system. The MRIsystem has a magnet to impress a polarizing magnetic field, a pluralityof gradient coils positioned about the bore of the magnet to impose amagnetic field gradient, and an RF transceiver system and an RF switchcontrolled by a pulse module to transmit RF signals to an RF coilassembly to acquire MR images. A transmit coil array having a pluralityof transmit coils is also disclosed. The apparatus also includes acomputer programmed to regulate RF power deposition on a subject (SAR)during MR imaging through independent control of the plurality oftransmit coils.

In accordance with another aspect of the invention, a method of MRimaging includes determining a region-of-interest within a subject andcontrolling RF excitation by a plurality of independent transmit coilsof a transmit coil array such that RF power deposition on the subject isreduced.

Various other features, objects and advantages of the present inventionwill be made apparent from the following detailed description and thedrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate one preferred embodiment presently contemplatedfor carrying out the invention.

In the drawings:

FIG. 1 is a schematic block diagram of an MR imaging system for use withthe present invention.

FIG. 2 is a block diagram illustrating a linear transmit coil arrayassembly in accordance with one aspect of the present invention.

FIG. 3 is a block diagram illustrating a wrap-around transmit coil arrayassembly in accordance with another aspect of the present invention.

FIG. 4 is a graph illustrating an RF excitation profile achievable witha transmit coil array in accordance with the present invention.

FIGS. 5-6 are plots illustrating k_(x)-direction weighting contributionby the coils of a transmit coil array positioned at two x-axislocations.

FIG. 7 illustrates the magnitude of localization profiles along thex-axis for each coil of a transmit coil array.

FIG. 8 graphically illustrates a pulse sequence in accordance with oneaspect of the present invention.

FIG. 9 illustrates resulting 2D transverse magnetization distribution asestimated by removing coil sensitivity weighting from an acquired image.

FIG. 10 illustrates B₁ field maps for the coils of an exemplary transmitcoil array.

FIG. 11 illustrates transverse magnetization distribution from anon-selective excitation in a reference body coil.

FIG. 12 illustrates B₁ field maps for each coil of a transmit coil arrayas well as a composite field map generated by superimposing theindividual B₁ field maps.

FIGS. 13-16 illustrate results of an RF pulsing protocol to control RFtransmission and minimize RF power deposition on a subject in accordancewith another aspect of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, the major components of a preferred magneticresonance imaging (MRI) system 10 incorporating the present inventionare shown. The operation of the system is controlled from an operatorconsole 12 which includes a keyboard or other input device 13, a controlpanel 14, and a display screen 16. The console 12 communicates through alink 18 with a separate computer system 20 that enables an operator tocontrol the production and display of images on the display screen 16.The computer system 20 includes a number of modules which communicatewith each other through a backplane 20 a. These include an imageprocessor module 22, a CPU module 24 and a memory module 26, known inthe art as a frame buffer for storing image data arrays. The computersystem 20 is linked to disk storage 28 and tape drive 30 for storage ofimage data and programs, and communicates with a separate system control32 through a high speed serial link 34. The input device 13 can includea mouse, joystick, keyboard, track ball, touch activated screen, lightwand, voice control, or any similar or equivalent input device, and maybe used for interactive geometry prescription.

The system control 32 includes a set of modules connected together by abackplane 32 a. These include a CPU module 36 and a pulse generatormodule 38 which connects to the operator console 12 through a seriallink 40. It is through link 40 that the system control 32 receivescommands from the operator to indicate the scan sequence that is to beperformed. The pulse generator module 38 operates the system componentsto carry out the desired scan sequence and produces data which indicatesthe timing, strength and shape of the RF pulses produced, and the timingand length of the data acquisition window. The pulse generator module 38connects to a set of gradient amplifiers 42, to indicate the timing andshape of the gradient pulses that are produced during the scan. Thepulse generator module 38 can also receive patient data from aphysiological acquisition controller 44 that receives signals from anumber of different sensors connected to the patient, such as ECGsignals from electrodes attached to the patient. And finally, the pulsegenerator module 38 connects to a scan room interface circuit 46 whichreceives signals from various sensors associated with the condition ofthe patient and the magnet system. It is also through the scan roominterface circuit 46 that a patient positioning system 48 receivescommands to move the patient to the desired position for the scan.

The gradient waveforms produced by the pulse generator module 38 areapplied to the gradient amplifier system 42 having G_(x), G_(y), andG_(z) amplifiers. Each gradient amplifier excites a correspondingphysical gradient coil in a gradient coil assembly generally designated50 to produce the magnetic field gradients used for spatially encodingacquired signals. The gradient coil assembly 50 forms part of a magnetassembly 52 which includes a polarizing magnet 54 and a whole-body RFcoil 56. A transceiver module 58 in the system control 32 producespulses which are amplified by an RF amplifier 60 and coupled to the RFcoil 56 by a transmit/receive switch 62. The resulting signals emittedby the excited nuclei in the patient may be sensed by the same RF coil56 and coupled through the transmit/receive switch 62 to a preamplifier64. The amplified MR signals are demodulated, filtered, and digitized inthe receiver section of the transceiver 58. The transmit/receive switch62 is controlled by a signal from the pulse generator module 38 toelectrically connect the RF amplifier 60 to the coil 56 during thetransmit mode and to connect the preamplifier 64 to the coil 56 duringthe receive mode. The transmit/receive switch 62 can also enable aseparate RF coil (for example, a surface coil) to be used in either thetransmit or receive mode.

The MR signals picked up by the RF coil 56 are digitized by thetransceiver module 58 and transferred to a memory module 66 in thesystem control 32. A scan is complete when an array of raw k-space datahas been acquired in the memory module 66. This raw k-space data isrearranged into separate k-space data arrays for each image to bereconstructed, and each of these is input to an array processor 68 whichoperates to Fourier transform the data into an array of image data. Thisimage data is conveyed through the serial link 34 to the computer system20 where it is stored in memory, such as disk storage 28. In response tocommands received from the operator console 12, this image data may bearchived in long term storage, such as on the tape drive 30, or it maybe further processed by the image processor 22 and conveyed to theoperator console 12 and presented on the display 16.

The present invention is directed to a method and system of acceleratingRF pulse transmission by a plurality of transmit coils. Such a transmitcoil array is illustrated in FIG. 2. Transmit coil array assembly 70includes a plurality of RF coils or elements 72 that are designed forparallel RF transmission, and a plurality of RF amplifiers 74. In onepreferred embodiment, each transmit coil 72 is driven by a dedicated RFamplifier 74. In this regard, each RF amplifier is configured togenerate a controlled current in a respective RF coil for defining andsteering an excitation volume 76 of a subject 78 within an MRI system.As will also be described, each of the transmit coils is controlled in amanner such that inter-coil correlations, i.e. mutual coupling, aretaken into account. As illustrated in FIG. 2, the transmit coils 72 arearranged in a substantially linear fashion. Additionally, as will bedescribed in greater detail, the RF amplifiers provide control signalsto the plurality of RF transmit coils such that induction of transversemagnetization may be localized to a particular region-of-interest so asto reduce RF power deposition on the subject. As will be furtherdescribed, each of the transmit coils is controlled in a manner suchthat RF power deposition is further reduced.

Referring now to FIG. 3, transmit coil array assembly 70 is illustratedin another embodiment. In this embodiment, the transmit coils 72 arepositioned in a wrap-around manner. In this regard, the coils arearranged in a distributed manner around the subject. Similar to thatshown and described with respect to FIG. 2, each RF coil 72 is connectedto a dedicated RF amplifier 74. One skilled in the art will readilyappreciate that FIGS. 2-3 illustrate a pair of possible arrangements ofthe coils of a transmit coil array and that other arrangements notspecifically illustrated are possible and contemplated.

As indicated above, the present invention is directed to a method andsystem operable with a transmit coil array such that RF excitation bythe transmit coils is carried out in parallel. This parallel excitationnot only supports a reduction in scan time through the acceleration ofRF pulses and the localization of targeted excitation, but also supportsreduction in RF power deposition on a subject.

The present invention will be described with respect to asmall-tip-angle excitation, but one skilled in the art will appreciatethat the present invention is extendable to other excitation regimes.The transverse magnetization resulting from a small-tip-angle excitationwith a single transmit coil may be analyzed by the Fourier transform ofthe k-space trajectory traversed and weighted during the excitation:M(x)=jγM ₀(x)b(x)∫_(k) W(k)S(k)e ^(j2πk·x) dk  Eqn. 1,where S(k) represents a spatial-frequency sampling trajectory controlledby the switching gradients, W(k), a spatial-frequency weighting inducedby the driving RF source, and b(x), a spatial weighting induced by thecoil's B₁ field pattern.

When several sets of pulse synthesizers and amplifiers form parallel RFsources that simultaneously drive corresponding coils during excitation,multiple spatial-frequency and spatial weightings influence the creationof the transverse magnetization. Within the limits of thesmall-tip-angle approximation, the k-space perspective expressed by Eqn.1 may be extended to analyze a parallel excitation system based on theproperty of linearity: $\begin{matrix}{{M(x)} = {{j\gamma}\quad{M_{0}(x)}{\sum\limits_{n = 1}^{N}{{b_{n}(x)}{\int_{k}{\sum\limits_{l = 1}^{N}\quad{c_{n,l}{W_{l}(k)}{S(k)}{\mathbb{e}}^{{j2\pi}\quad{k \cdot x}}\quad{{\mathbb{d}k}.}}}}}}}} & {{Eqn}.\quad 2}\end{matrix}$In Eqn. 2, N denotes the total number of transmit coils, n and l arecoil indices, c_(n,l) are coefficients characterizing the mutualcoupling between the coils, W_(l)(k) represent spatial-frequencyweightings induced by the independently controlled RF sources, andb_(n)(x) represent spatial weightings induced by the coils respective B₁field patterns.

With g(x) denoting the term in Eqn. 2 that defines the excitationprofile, g(x) may be expressed as $\begin{matrix}\begin{matrix}{{g(x)} = {\underset{l = 1}{\overset{N}{\sum\quad}}{\left( {\sum\limits_{n = l}^{N}{c_{n,l}{b_{n}(x)}}} \right){\int_{k}{{W_{l}(k)}{S(k)}{\mathbb{e}}^{{j2\pi}\quad{k \cdot x}}\quad{\mathbb{d}k}}}}}} \\{{= {\sum\limits_{l = 1}^{N}\quad{{{\hat{b}}_{l}(x)}{\int_{k}{{W_{l}\quad(k)}{S(k)}{\mathbb{e}}^{{j2\pi}\quad{k \cdot x}}{\mathbb{d}k}}}}}},}\end{matrix} & {{Eqn}.\quad 3}\end{matrix}$which indicates that in the analysis of the parallel transmit system,$\quad{{{{\hat{b}}_{l}(x)} \equiv {\sum\limits_{n = 1}^{N}{c_{n,l}{b_{n}(x)}}}},}$the effective spatial weightings, may be used to account forcoupling-induced inter-coil correlations.

As an example, a 2D excitation case is considered, where an echo planar(k_(x),k_(y)) trajectory, with k_(x) being the slow direction and Δ_(kx)being the sampling period, is used and {(x,y)|x_(min)≦x≦x_(max),y_(min)≦y≦y_(max)} specifies the field-of-view that contains thesubject. The k-space weighting and sampling gives rise to a 2Dexcitation profile, which, as defined by Eqn. 3, is a weightedsuperposition of N periodic functions: $\begin{matrix}{{g\left( {x,y} \right)} = {\sum\limits_{l = 1}^{N}{{{\hat{b}}_{l}\left( {x,y} \right)}{\sum\limits_{m = {- \infty}}^{+ \infty}{{u_{l}\left( {{x - {m\quad\Delta}},y} \right)}.}}}}} & {{Eqn}.\quad 4}\end{matrix}$In Eqn. 4, the notation u_(l)(x) and Δ represent, respectively,∫W_(l)(k)e^(j2πk·x)dk and 1/Δ_(kx). Z-dependence has been suppressed forsimplicity.

From Eqn. 4, it is clear that the discrete nature along k_(x)necessarily implies aliasing lobes along x. Of significance, Eqn. 4indicates that side lobe suppression may be achieved through multipleweighting in the spatial ({circumflex over (b)}_(l)(x)) andspatial-frequency (W_(l)(k)) domains. This can be compared to the caseof excitation with a body-coil (volume coil with b(x)≈1), where atypical pulse design has the side lobes pushed outside the subject bylimiting sampling period Δ_(kx) to be no greater than 1/D(D=x_(max)−x_(min)).

Within a small-tip-angle regime, design of gradient and RF pulses givena desired excitation profile may be achieved solving an inverse problemdefined by Eqn. 3. For the purpose of illustration, a 2D excitation willbe described.

To achieve a 2D excitation profile given by g(x,y) and with solutions oftype: u_(l)(x,y)=h_(l)(x,y)g(x,y), Eqn. 4 may be rewritten as:$\begin{matrix}{{{g\left( {x,y} \right)} = {\sum\limits_{m = {- \infty}}^{+ \infty}{{g\left( {{x - {m\quad\Delta}},y} \right)}{\sum\limits_{l = 1}^{N}{{h_{l}\left( {{x - {m\quad\Delta}},y} \right)}{{\hat{b}}_{l}\left( {x,y} \right)}}}}}},} & {{Eqn}.\quad 5}\end{matrix}$which in general requires, for all (x,y) inside the field-of-view,$\begin{matrix}{{\sum\limits_{l = 1}^{N}{{h_{l}\left( {{x - {m\quad\Delta}},y} \right)}{{\hat{b}}_{l}\left( {x,y} \right)}}} = \left\{ {\begin{matrix}{1,} & {m = 0} \\{0,} & {otherwise}\end{matrix}.} \right.} & {{Eqn}.\quad 6}\end{matrix}$

By sorting the equations (e.g., through change of variables), it can beshown that {h_(l)(x,y), l=1, . . . , N} is typically constrained, ateach (x,y), by K linear equations (K is defined as the smallest integerthat is greater or equal to D/Δ):C _((x,y)) h _((x,y)) =e ₁  Eqn. 7,where $\begin{matrix}{{C_{({x,y})} = \begin{bmatrix}{{\hat{b}}_{1}\left( {x,y} \right)} & {{\hat{b}}_{2}\left( {x,y} \right)} & \ldots & {{\hat{b}}_{N}\left( {x,y} \right)} \\\vdots & \vdots & \quad & \vdots \\{{\hat{b}}_{1}\left( {{x + {m\quad\Delta}},y} \right)} & {{\hat{b}}_{2}\left( {{x + {m\quad\Delta}},y} \right)} & \ldots & {{\hat{b}}_{N}\left( {{x + {m\quad\Delta}},y} \right)} \\\vdots & \vdots & \quad & \vdots\end{bmatrix}},} & {{Eqn}.\quad 8}\end{matrix}$  h _((x,y)) =[h ₁(x,y) h ₂(x,y) . . . h_(N)(x,y)]^(T)  Eqn. 9,e₁=[1 0 . . . ]^(T)  Eqn. 10,and {x, . . . , x+mΔ (m≠0), . . . } represents the set of x coordinateswithin the field-of-view that are evenly spaced and inter-associated dueto aliasing. Employing a sampling period Δ_(kx) that is greater than1/D, all but the first equation in Eqn. 7 represent the suppression ofaliasing side lobes located within the field-of-view.

Solving Eqn. 7 repeatedly for locations throughout the field-of-viewyields h_(l)(x,y)'s, which then allow the calculation of k-spaceweighting according to the following:W _(l)(k)=∫_(x) h _(l)(x)g(x)e ^(−j2πk·x) dx  Eqn. 11.The k-space weighting, and the RF pulse waveform associated with the lthcoil, can thus be calculated with the Fourier transform of aspatially-weighted version of the desired excitation profile, where thespatial weighting is derived from B₁ field maps of each transmit coiland the k-space traversing trajectory.

Quality of B₁ field maps has a direct impact on excitation profileaccuracy. The maps may be experimentally calibrated one at a time. Withthis approach, each calibration may involve an imaging experiment thatuses a single element of the transmit array for transmission (with zeroinputs to other elements) and the body coil for reception. A division ofthe result by a reference image for removing the modulation of subjectcontrast and additional processing for suppressing the effects of noise,then provides an estimate of the effective B₁ map associated with thetransmit element. Alternatively, B₁ maps may be inferred fromsensitivity maps based on the principle of reciprocity. It should benoted that multiple sensitivity maps may be calibrated in parallel toreduce calibration time. However, the opposite phase and possiblechanges in coil coupling characteristics between transmit and receive,if not accounted for, may compromise the accuracy of the estimatedeffective B₁ maps.

Comparing two types of systems in the 2D excitation example, the presentinvention provides excitation acceleration of up to N-fold over asingle-channel body-coil system. Formally, this is revealed by the factthat Eqn. 7 admits at least one solution if N≧D/Δ, or equivalently,Δ_(kx)≦N/D, which is in contrast to the more stringent requirement ofΔ_(kx)≦1/D in the case of body-coil transmission. Intuitively, thecapacity for acceleration, or, reduction in excitation k-space samplingdensity, is probably best appreciated by recognizing that while areduction in excitation k-space sampling density causes aliasing lobesto locate inside the subject, an appropriate design of thespatial-frequency domain weighting (W_(l)(k)) can combine with thespatial domain weighting ({circumflex over (b)}_(l)(x)) and the aliasingpattern (as determined by the sampling) to cause incoherent addition,therefore realizing reduction or annihilation of aliasing lobes' netamplitudes.

For an acceleration factor that is smaller than N, or equivalently, asampling period that is smaller than N/D, Eqn. 7 allows a family ofsolutions of dimensionality N−K. This results in choices of excitationpulse designs that are all capable of producing a main lobe that matchesthe desired excitation profile and, when applicable, simultaneouslysuppressing aliasing lobes. The specific design that uses h_(l)(x,y)'scalculated by solving Eqn. 7 in the minimum norm sense is notable sinceit tends to lessen the sensitivity of the excitation profile toperturbations or reduces the power requirement on the RF amplifiers.

The independent driving of transmit coils of a transmit coil array alsosupports SAR management. Compared to uniform coverage of a subjectvolume with a single transmit coil, focused excitation of only theregion-of-interest with an array of distributed local transmit coils byemploying the coils in close proximity prevents substantial RF powerdeposition beyond the region. In addition, from the many ways oforchestrating the sources and achieving a desired excitation profile,the one that induces an E field with as small as possible an ensuing RFpower deposition can be chosen.

While the present invention supports a number of SAR reductiontechniques, i.e. focused RF excitation, SAR management with a focus onthe minimization of SAR averaged over the subject volume and theexcitation period, which is defined by: $\begin{matrix}{{{SAR}_{ave} = {\frac{1}{P}{\sum\limits_{p = 0}^{P - 1}{\frac{1}{V}{\int{\frac{\sigma(x)}{2{\rho(x)}}{{E\left( {x,{p\quad\Delta\quad t}} \right)}}^{2}{\mathbb{d}v}}}}}}},} & {{Eqn}.\quad 12}\end{matrix}$will be hereinafter described in greater detail. In Eqn. 12, σ denotestissue conductivity; ρ, density; V, the size of the irradiated subjectvolume; and P, the total number of time points used to quantify thetemporal average.

Given, for example, multiple loop coils placed facing the surface of alarge slab of conducting material. At low frequencies, the fields insidethe slab tend to be dominated by the incident fields, which are producedby the currents in the coils. Following a quasi-static approach inanalyzing electric and magnetic near-fields, the fields may becharacterized with a vector potential A: $\begin{matrix}{{A = {\sum\limits_{l = 1}^{N}{\frac{\mu\quad I_{l}}{4\pi}{\oint_{C_{l}^{\prime}}\frac{{ds}^{\prime}}{{x - x^{\prime}}}}}}},} & {{Eqn}.\quad 13}\end{matrix}$where the line integrals over the currents in the coils are based onfilament approximation of the coil conductors, and the fields arerelated to A by B=∇×A and E=−dA/dt. In this case, the |E(x,pΔt)|² termin Eqn. 12 may be evaluated as: $\begin{matrix}{\begin{matrix}{{{E\left( {x,{p\quad\Delta\quad t}} \right)}}^{2} = {{{- {j\omega}}\quad{A\left( {x,{p\quad\Delta\quad t}} \right)}}}^{2}} \\{= {{\sum\limits_{l = 1}^{N}{{I_{l}\left( {p\quad\Delta\quad t} \right)}\left( {\frac{- {j\omega\mu}}{4\pi}{\oint_{C_{l}^{\prime}}\frac{{ds}^{\prime}}{{x - x^{\prime}}}}} \right)}}}^{2}} \\{= {{\sum\limits_{l = 1}^{N}{{I_{l}\left( {p\quad\Delta\quad t} \right)}{\Phi_{l}(x)}}}}^{2}}\end{matrix},} & {{Eqn}.\quad 14}\end{matrix}$which is a quadratic form in [I₁(pΔt) I₂(pΔt) . . . I_(N)(pΔt)], avector with values of the current waveforms at time pΔt. Sorting out thevolume integral and temporal summation, SAR_(ave) may be expressed as aquadratic function in the samples of the current waveforms:SAR _(ave) =s ^(H) Fs  Eqn. 15,where superscript H denotes conjugate transpose, matrix F carriesentries evaluated based on Eqns. 12 and 14, and vector s collects in acorresponding order a total of N×P samples of the current waveforms.

Provided that the electric field scales linearly with applied sourcefunctions, a quadratic relationship in the form of Eqn. 5 betweenaverage SAR and source function samples generally holds. In the presenceof biological objects or at high frequencies however, solving Maxwell'sequations is difficult and construction of the F matrix may need to relyon calibration results or direct E field measurements.

Given the dependencies of the absorption rate and transversemagnetization on the applied source functions, the determination of aset of coordinated source functions that produces the desired excitationprofile while inducing minimum SAR is possible. In the small tip angleregime or its extension where a linear treatment of the Bloch equationsis appropriate, closed-form solution exists for multi-dimensionalexcitation design, which obviates the task of searching a vast designspace.

Continuing with the previously described 2D excitation example,equations of the form of Eqn. 7, which stem from the requirement ofcreating the desired main lobe in the subject while avoiding aliasinglobes, collectively constrain the spatial patterns of h_(l)(x)'s.Pooling these equations together thus gives the design constraints,which, in a matrix form, may be expressed as:C _(all) h _(all) =e _(all)  Eqn. 16.In Eqn. 16, C_(all) is a block-diagonal matrix with C_((x,y))'s on thediagonal and zeros everywhere else, and h_(all) and e_(all) are vectorsrepresenting, respectively, concatenated h_((x,y))'s and e₁'s. If amoving sample of the weighting functions is carried out at a constantrate, the W_(l)(k(t))'s are proportional to the current waveforms. TheFourier transform relationship between the W_(l)(k)'s and the h_(l)(x)'sallows rewriting Eqn. 15 in terms of h_(all):SAR _(ave) =h _(all) ^(H) Vh _(all)  Eqn. 17.The quadratic form remains as Fourier transform defines a linear mappingfrom h_(l)(x) to W_(l)(k). A variable sample rate would only modifyentries of matrix V to match gradient amplitude changes. As such, pulsedesign for SAR management may be achieved by minimizing a quadraticfunction subject to a linear constraint:minimize h_(all) ^(H)Vh_(all)subject to C _(all) h _(all) =e _(all)  Eqn. 18,which may be solved using well-known numerical techniques.

Design principles for small-tip-angle parallel excitation pulses such asthat described above were evaluated in simulation and phantomexperiments. To evaluate the design principle for acceleratedmulti-dimensional excitation, parallel excitation with a transmit coilarray was first examined in a simulation study. The transmit array wascomprised of nine identical 19.8 cm×6.4 cm loop coils that were placedon a flat form and lined up along the x-direction. This array faced athin slab object below the array surface. 2D excitation with a desiredexcitation profile across the object in the form ofg(x)=g_(x)(x)·g_(z)(z) was approached with parallel excitation pulses.In this case, use of an echo planar k_(x)−k_(z) trajectory consisting ofk_(x)=constant lines evenly spaced by Δ_(kx), the negligible y- andz-direction B₁ variation in the localized volume, and the separabilityof g(x) yielded solutions to Eqn. 11 of the formW_(l)(k)=U_(kx,l)(k_(x))·U_(kz)(k_(z)), whereU _(kx,l)(k _(x))=∫_(x) h _(l)(x)g _(x)(x)e ^(−j2πxk) ^(x) dx.U _(kz)(k _(z))=∫_(z) g _(z)(z)e ^(−j2πzk) ^(z) dzFor purposes of this first experiment equations of form Eqn. 7 wereconstructed and weightings over k_(x)−k_(z) were determined. RF pulsewaveforms were then calculated based on Eqn. 11. As a reference,body-coil excitation pulses aimed at the same 2D localization weredesigned.

The design principle for accelerated excitation was further evaluated ina phantom study, which was carried out on a 1.5 Tesla MRI scanner (CVi,GE Medical Systems, Waukesha, Wis.) with a setup very similar to that ofthe simulation study noted above. The transmit coil array of interestwas of the same geometry and placed 3 cm above a water-filled 41×19×1cm³ brick phantom. As the scanner only supported single-channel RF pulsetransmission, the study examined parallel excitation indirectly, bymimicking simultaneous driving of the nine array elements through aseries of nine single-channel experiments. Validity of the approach isensured by the property of linearity in the small-tip-angle regime,which allows the prediction of the result of a parallel excitationexperiment from the superposition of transverse magnetizationdistributions observed from single-channel excitation experiments.

Specifically, a single transmit/receive loop coil of size 19.8 cm×6.4 cmwas attached to the scanner's RF interface. During the nine experiments,the coil was placed and driven one configuration at a time, each with aposition and RF pulse corresponding to one of the nine elements on thevirtual coil array that were desired to simulate. After completion ofevery transmission, the coil was immediately switched to the receivefunction, whereas throughout the experiments the scanner's body coil waskept detuned. 2D excitation and acquisition were carried out with agradient echo sequence. From one experiment to another, excitationk-space traversing was kept the same (i.e., echo planar k_(x)−k_(z)trajectory with k_(x) being the slow direction) but the weighting (RFpulse) was changed according to the excitation pulse design. 2Dacquisition produced images that mapped out the water phantom along thex and z directions (and projected along y, the normal direction of the 1cm slab). 2D transverse magnetization distributions were quantified byremoving the coils' sensitivity profiles from the images. Thedistributions were then superimposed to provide an estimate of thedistribution resulting from the corresponding parallel excitationexperiment. By the design of the study, coil coupling is not a factor.B₁ maps that were estimated based on Biot-Savart Law were used in boththe RF pulse calculations and the sensitivity profile removal.

In another study on excitation acceleration, an all-around arraygeometry was examined. The array consisted of seven transmit elementsthat were distributed azimuthally on a wrap-around form inside ascanner's patient bore. Computer simulations evaluated 2D excitationdesigns that localize along both x and y dimensions. Coupling betweenelements was not negligible and was taken into account with a couplingmatrix determined from mutual inductance calculations. The designs usedthe original Eqns. 7 and 11.

Effectiveness of the SAR management scheme described previously asintegrated in the parallel pulse design was further evaluated. Theevaluation was carried out in the same fashion as the first simulationstudy except for the application of parallel excitation pulses of designtype defined by Eqn. 18 instead of Eqn. 7. With the calculatedh_(l)(x,z)'s, Eqn. 11 gave weightings over k_(x)−k_(z), which in turndetermined RF pulse waveforms. The resulting excitation profile andaverage SAR were compared to that of the first simulation study.

A discussion of the results of the above-described experiments follow.Focused excitation of a 5 cm by 5 cm region centered at x=8 cm and z=0inside the slab object was investigated in the first simulation study.Based on a body transmit coil, a reference design employed pulses thattraversed 57 k_(x)=constant lines at Δ_(kx)=1/31.6 cycles/cm. Thex-direction localization that resulted from this reference design isshown in FIGS. 4-7. A parallel excitation design accomplished the 2Dlocalization task with the transmit coil array. Representing a 4-foldacceleration, the design employed pulses that traversed 14k_(x)=constant lines at Δ_(kx)=1/7 cycles/cm. U_(kx,4)(mΔ_(kx)) andU_(kx,7)(mΔ_(kx)), the k_(x)-direction weighting contributed by thecoils positioned at x=−4 cm and x=8 cm, respectively, are illustrated inFIG. 5 and FIG. 6. Localization along x due to each of the nine coils isshown in FIG. 7. Note that while the first aliasing side lobes were 4.5times closer to the target (center-to-center spacing=7 cm) as a resultof the sampling density reduction, the net amplitudes of these as wellas other aliasing lobes located inside the 40 cm FOV were negligible dueto incoherent addition, as shown in FIG. 4. Compared to the result ofthe body-coil approach, localization of the parallel excitation was aswell refocused (the imaginary component, not shown, was negligible) andof comparable spatial resolution. See FIG. 4.

In the phantom study, effects of incoherent addition on aliasing sidelobes were the focus of investigation. To this end, 2D excitation pulseswere designed to target a region in the water phantom directly below thecenter element. To facilitate the investigation, pulse calculationsfurther assumed an extended linear array instead of the 9-element one.The designed pulses were 5.7 msec in length. For the center elementexperiment, FIG. 8 shows the applied RF pulse (magnitude and phase) aswell as G_(x) and G_(z), the gradient pulses identically executed in allthe experiments of the series. Removing the coil's sensitivity profilefrom the resulting image provided an estimate of the 2D transversemagnetization distribution induced by the element, as shown in FIG. 9.FIG. 10 illustrates the B₁/sensitivity maps used. As a reference, FIG.11 illustrates the transverse magnetization distribution from anonselective excitation in a body-coil transmit-receive experiment.Noticeable in FIG. 9 is a noise amplification effect due to the divisionoperation employed for sensitivity profile removal, which tends toincrease in severity farther away from the sensitive region. To preventexcessive noise amplification from obscuring the investigation, thedivision operation was suppressed in distant regions.

Results from all nine experiments are summarized in FIG. 12, whichdisplays in rows 1 through 9 the mapped transverse magnetizationcorresponding to each of the experiments. The bottom row (row 10)presents the result of superimposing the individual maps, intended as aprediction of the result of a corresponding parallel excitation. Again,substantial reduction of aliasing side lobes due to incoherent additionwas observed. With the setup, contributions from the elements in theestablishment of the main lobe and the suppression of the aliasing lobeswere readily appreciated. The results from the center element alone andfrom the middle five and middle nine elements, suggest that localexcitation profile control is mainly achieved through nearby coils. Useof the extended array assumption in the pulse calculations accounted formuch of the residual aliasing (incomplete annihilation) towards the9-element array's boundary. Augmenting the array with elements beyondthe nine can rectify this effect. Designing pulses for the 9-elementarray can rid this effect too, in which case boundary coils' weightingwould experience the greatest changes.

2D parallel excitation pulses for a wrap-around array were designed andevaluated. The simulations concentrated on the task of selectivelyexciting an arbitrarily positioned local volume within a 40 cm-by-23 cmaxial field-of-view. Eqn. 7 was solved repeatedly based on the effectiveB₁ field patterns and an EPI trajectory comprising 14 k_(x)=constantlines at Δ_(kx)=1/6.9 cycles/cm. For the lth coil, l=1, 2, . . . , 7,the product of the desired 2D localization profile with the calculatedh_(l)(x,y) was then Fourier transformed to derive the coil's k-spaceweighting and RF pulse waveform by the parallel excitation. The netresult was substantially free of aliasing side lobes and represents anexcellent match to that of a reference excitation, which involvedbody-coil transmission of a 4-times longer conventional RF pulse.

The design of the last simulation study resulted in parallel excitationpulses that differed in shape from the pulses of the first simulationstudy. FIGS. 13-16 present the outcome with a format similar to that ofFIGS. 4-7. While the pulses maintained the same level of localizationaccuracy and spatial resolution as that of the pulses of the firstsimulation study, FIG. 13, the design changes led to a 38% reduction inaverage SAR, confirming the substantial impact of the integrated SARmanagement scheme.

With the present invention, designed RF pulses are synthesized,amplified and fed to corresponding transmit elements in parallel toinduce both spatial and temporal variations of the composite B₁ field,which, accompanied by appropriate gradient changes played out insynchrony, create a desired excitation profile upon completion ofexcitation. This is in contrast to a conventional approach, where thedesign of coil geometry and the offsets of driving-port phase/magnitudetarget B₁-field spatial homogeneity, and an RF pulse played duringexcitation is limited to manipulate B₁-field temporal variation only.One skilled in the art will recognize that inducing appropriate B₁spatiotemporal variations for excitation bears significant ramificationson RF excitation performance. That is parallel excitation accommodatesexcitation acceleration and/or SAR control without substantial sacrificein the accuracy of producing the desired excitation profile.

In summary, the RF pulse driving a transmit element can be calculatedwith the Fourier transform of a spatially weighted version of thedesired excitation profile, the capacity for acceleratingmulti-dimensional excitation by the means of k-space sampling densityreduction lies with the suppression of aliasing lobes and can beachieved by appropriately designed driving pulses (spatial-frequencydomain weightings), and SAR management can be accomplished by minimizinga quadratic function in the driving sources, which searches a way oforchestrating the sources to achieve a desired excitation profile and/oracceleration while inducing an E field with minimum ensuing RF powerdeposition.

From an application perspective, fast imaging is an area where thepresent parallel excitation approach is particularly applicable. Undercircumstances where the anatomy of interest is contained in a localregion for example, multi-dimensional excitation that “spotlights” theregion allows acceleration of imaging by alleviating the burden ofspatial encoding inflicted on signal acquisition. Representingimprovements over conventional excitations, multi-fold shorter parallelexcitations support imaging volume definition/steering while breakingthe time cost barrier that hindered the practical use ofmulti-dimensional pulses in the past. Compared to the use of a parallelacquisition approach, focused imaging based on the parallel excitationapproach is not subject to the unique SNR degradation described by thegeometric factor. Combined use of the two approaches is possible and canprovide an even greater capacity for scan time reduction. While theexperiments reported here focused on 2D localization, the parallelexcitation approach applies to the creation and acceleration of general2D excitation profiles, with utilities including correction for fieldimperfection-induced effects and non-Fourier spatial encoding. Thepresent invention is also applicable to 3D acquisition.

In high field imaging, the transmit system and driving means describedmay be used to both manage excitation profile and regulate RF powerdeposition. Embodying an integrated treatment of excitation pulses andtransmit coils, the present invention facilitates excitation profilecontrol. Transmission with a distributed parallel system, accelerationof excitation and management of SAR further provides a solution to powerdeposition at high field strength.

Therefore, in accordance with one embodiment, the invention is embodiedin a computer program stored on a computer readable storage medium andhaving instructions which, when executed by a computer, cause thecomputer acquire a B₁ field map for each transmit coil of a transmitcoil array and determine from the B₁ field maps a spatiotemporalvariation of a composite B₁ field. The computer is also caused togenerate an RF pulsing sequence tailored to each respective transmitcoil such that RF power deposition during imaging is reduced.

According to another aspect, the present invention includes an MRIapparatus comprising a magnetic resonance imaging (MRI) system. The MRIsystem has a magnet to impress a polarizing magnetic field, a pluralityof gradient coils positioned about the bore of the magnet to impose amagnetic field gradient, and an RF transceiver system and an RF switchcontrolled by a pulse module to transmit RF signals to an RF coilassembly to acquire MR images. A transmit coil array having a pluralityof transmit coils is also disclosed. The apparatus also includes acomputer programmed to regulate RF power deposition on a subject (SAR)during MR imaging through independent control of the plurality oftransmit coils.

In accordance with another aspect of the invention, a method of MRimaging includes determining a region-of-interest within a subject andcontrolling RF excitation by a plurality of independent transmit coilsof a transmit coil array such that RF power deposition on the subject isreduced.

The present invention has been described in terms of the preferredembodiment, and it is recognized that equivalents, alternatives, andmodifications, aside from those expressly stated, are possible andwithin the scope of the appending claims.

1-23. (canceled)
 24. A computer readable storage medium having acomputer program stored thereon and representing a set of instructionsthat when executed by a computer causes the computer to: acquire a B₁field map for each transmit coil of a transmit coil array, the transmitcoil array capable of having any transmit coil array geometry; determinefrom the B₁ field maps a spatiotemporal variation of a composite B₁field; and generate an RF pulsing sequence tailored to a respectivetransmit coil such that RF power deposition during MR imaging isminimized.
 25. The computer readable storage medium of claim 24 whereinthe set of instructions further causes the computer to minimize RF powerdeposition across an imaging volume without causing substantialdeviation of a RF excitation profile created by the transmit coil arrayfrom a desired excitation profile.
 26. The computer readable storagemedium of claim 24 wherein the set of instructions causes the computerto determine an RF pulse scheme for a transmit coil based on at least aneffective B₁ field for the transmit coils.
 27. The computer readablestorage medium of claim 26 wherein each effective B₁ field reflectsmutual coupling of a transmit coil and at least another transmit coil.28. The computer readable storage medium of claim 24 wherein the set ofinstructions further causes the computer to design each pulsing sequencesuch that parallel RF excitation with the transmit coil array produces aresult that is consistent with a desired excitation profile.
 29. Thecomputer readable storage medium of claim 24 wherein the set ofinstructions further causes the computer to acquire 2D or 3D MR data.30. The computer readable storage medium of claim 24 wherein thetransmit coil array includes a linearly arranged plurality of transmitcoils.
 31. The computer readable storage medium of claim 30 wherein eachtransmit coil is driven by a dedicated RF amplifier.
 32. An MRIapparatus comprising: a magnetic resonance imaging (MRI) system having amagnet to impress a polarizing magnetic field, a plurality of gradientcoils positioned about a bore of the magnet to induce a magnetic fieldgradient, a transmit coil array having a plurality of transmit coils,and an RF transceiver system and an RF switch controlled by a pulsemodule to transmit RF signals to an RF coil assembly to acquire MRimages; and a computer programmed to: design an RF pulse waveform foreach transmit coil of a plurality of transmit coils of a transmit coilarray such that side lobes in a parallel RF excitation by the transmitcoil array are reduced; and regulate RF power deposition on a subjectduring MR imaging through independent control of the plurality oftransmit coils of the transmit coil array.
 33. The MRI apparatus ofclaim 32 wherein the computer is further programmed to simultaneouslyachieve RF excitation consistent with a desired excitation profile andSAR reduction on the subject.
 34. The MRI apparatus of claim 32 whereinthe computer is further programmed to control RF excitation of thetransmit coil array to focus RF excitation on a region-of-interestwithin the subject.
 35. The MRI apparatus of claim 32 wherein thecomputer is further programmed to design an RF pulse waveform for atransmit coil based on at least an effective B₁ field generated by thetransmit coil.
 36. The MRI apparatus of claim 32 wherein the computer isfurther programmed to acquire 2D or 3D MR data.
 37. The MRI apparatus ofclaim 32 wherein the plurality of transmit coils of the transmit coilarray is linearly arranged.
 38. The MRI apparatus of claim 32 whereineach transmit coil is driven by a dedicated RF amplifier.
 39. A methodof MR imaging comprising the steps of: determining a region-of-interestin an imaging volume; determining an RF pulse scheme for each transmitcoil of a plurality of transmit coils of a transmit coil array based onat least an effective B₁ field for each transmit coil, wherein eacheffective B₁ field includes data regarding mutual coupling of theplurality of transmit coils of the transmit coil array; andindependently controlling RF excitation by the plurality of transmitcoils of the transmit coil array such that RF power deposition isreduced.
 40. The method of claim 39 further comprising the step ofindependently controlling RF excitation by the plurality of transmitcoils such that RF power absorption by a subject disposed in the imagingvolume is minimized on average over the imaging volume.
 41. The methodof claim 40 further comprising the step of minimizing RF powerdeposition over the imaging volume without causing substantial deviationof a parallel RF excitation profile created by the transmit coil arrayfrom a desired excitation profile.
 42. The method of claim 39 furthercomprising the step of minimizing RF power deposition, which embodies aprinciple that is applicable to any transmit coil array geometry.
 43. Acomputer readable storage medium having a computer program storedthereon and representing a set of instructions that when executed by acomputer causes the computer to: acquire a B₁ field map for eachtransmit coil of a transmit coil array; determine from the B₁ field mapsa spatiotemporal variation of a composite B₁ field; determine an RFpulse scheme for a transmit coil based on at least an effective B₁ fieldfor the transmit coils, wherein each effective B₁ field reflects mutualcoupling of a transmit coil and at least another transmit coil; andgenerate an RF pulsing sequence tailored to a respective transmit coilsuch that RF power deposition during MR imaging is reduced.